Abstract

The periodic structure on the optical surface affects the beam shape and its propagation. As the size of the optical elements becomes larger and its shape becomes complicated, the quantitative analysis of the effect of the periodic structure on the optical surface becomes indispensable given that it is very difficult to completely eliminate the microscopic periodic structures. Herein, we have experimentally investigated Bragg scattering from an optical surface with extremely small aspect ratios (~10−5) and groove densities (0.5 lines/mm). We observed the period of the constructive interference formed due to the propagation of the 0th, 1st, and −1st beam modes caused by Bragg scattering. When the periodic structure has a modulation depth of ± 50 nm, the intensity increase of constructive interference between the beam modes formed by Bragg scattering was > 10 times greater than the intensity of a flat surface at the propagation distance at which constructive interference was most pronounced. This study is envisaged to open new avenues for the quantification of the effect of periodic structures based on the observation of the interference on the beam profile formed by Bragg scattering during the beam propagation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

F. Siewert, J. Buchheim, G. Gwalt, R. Bean, and A. P. Mancuso, “On the characterization of a 1 m long, ultra-precise KB-focusing mirror pair for European XFEL by means of slope measuring deflectometry,” Rev. Sci. Instrum. 90(2), 021713 (2019).
[Crossref] [PubMed]

C. L. He and W. J. Zong, “Diffraction effect and its elimination method for diamond-turned optics,” Opt. Express 27(2), 1326–1344 (2019).
[Crossref] [PubMed]

2018 (3)

M. Wen, I. V. Kozhevnikov, F. Siewert, A. V. Buzmakov, C. Xie, Q. Huang, Z. Wang, L. Samoylova, and H. Sinn, “Effect of the surface roughness on X-ray absorption by mirrors operating at extremely small grazing angles,” Opt. Express 26(16), 21003–21018 (2018).
[Crossref] [PubMed]

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

J. Kim, H.-Y. Kim, J. Park, S. Kim, S. Kim, S. Rah, J. Lim, and K. H. Nam, “Focusing X-ray free-electron laser pulses using Kirkpatrick-Baez mirrors at the NCI hutch of the PAL-XFEL,” J. Synchrotron Radiat. 25(Pt 1), 289–292 (2018).
[Crossref] [PubMed]

2017 (2)

2015 (1)

2014 (1)

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
[Crossref] [PubMed]

2013 (2)

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

Y. Chu, X. Liang, L. Yu, Y. Xu, L. Xu, L. Ma, X. Lu, Y. Liu, Y. Leng, R. Li, and Z. Xu, “High-contrast 2.0 Petawatt Ti:sapphire laser system,” Opt. Express 21(24), 29231–29239 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

2010 (3)

J. H. Sung, S. K. Lee, T. J. Yu, T. M. Jeong, and J. Lee, “0.1 Hz 1.0 PW Ti:sapphire laser,” Opt. Lett. 35(18), 3021–3023 (2010).
[Crossref] [PubMed]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

L. Li, S. A. Collins, and A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” J. Manuf. Sci. Eng. 132(2), 021002 (2010).
[Crossref]

2007 (2)

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[Crossref]

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Technol. 39(2), 268–274 (2007).
[Crossref]

2004 (1)

2003 (1)

2002 (1)

2001 (1)

C. F. Cheung and W. B. Lee, “Characterization of nanosurface generation in single-point diamond turning,” Int. J. Mach. Tools Manuf. 41(6), 851–875 (2001).
[Crossref]

2000 (2)

B. B. Oreb, D. I. Farrant, C. J. Walsh, G. Forbes, and P. S. Fairman, “Calibration of a 300-mm-aperture phase-shifting Fizeau interferometer,” Appl. Opt. 39(28), 5161–5171 (2000).
[Crossref] [PubMed]

C. F. Cheung and W. B. Lee, “A theoretical and experimental investigation of surface roughness formation in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 40(7), 979–1002 (2000).
[Crossref]

1998 (1)

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

1995 (3)

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, “Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75(15), 2823–2826 (1995).
[Crossref] [PubMed]

D. M. Giltner, R. W. McGowan, and S. A. Lee, “Atom interferometer based on Bragg scattering from standing light waves,” Phys. Rev. Lett. 75(14), 2638–2641 (1995).
[Crossref] [PubMed]

1988 (1)

B. G. Oldaker, A. H. Miklich, D. E. Pritchard, D. E. Pritchard, and Mar- PJ p tin, “Bragg scattering of atoms from a standing light wave,” Phys. Rev. Lett. 60(6), 515–518 (1988).
[Crossref] [PubMed]

1967 (1)

E. P. Ippen, “Diffraction of light by surface acoustic waves,” Proc. IEEE 55(2), 248–249 (1967).
[Crossref]

1913 (1)

W. L. Bragg and W. L. Bragg, “The reflection of X-rays by crystal,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 88(605), 428–438 (1913).
[Crossref]

Akahane, Y.

Aoyama, M.

Bahk, S.-W.

Bean, R.

F. Siewert, J. Buchheim, G. Gwalt, R. Bean, and A. P. Mancuso, “On the characterization of a 1 m long, ultra-precise KB-focusing mirror pair for European XFEL by means of slope measuring deflectometry,” Rev. Sci. Instrum. 90(2), 021713 (2019).
[Crossref] [PubMed]

Bhaduri, B.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Technol. 39(2), 268–274 (2007).
[Crossref]

Birkl, G.

G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, “Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75(15), 2823–2826 (1995).
[Crossref] [PubMed]

Bragg, W. L.

W. L. Bragg and W. L. Bragg, “The reflection of X-rays by crystal,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 88(605), 428–438 (1913).
[Crossref]

W. L. Bragg and W. L. Bragg, “The reflection of X-rays by crystal,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 88(605), 428–438 (1913).
[Crossref]

Bruder, J.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[Crossref]

Buchheim, J.

F. Siewert, J. Buchheim, G. Gwalt, R. Bean, and A. P. Mancuso, “On the characterization of a 1 m long, ultra-precise KB-focusing mirror pair for European XFEL by means of slope measuring deflectometry,” Rev. Sci. Instrum. 90(2), 021713 (2019).
[Crossref] [PubMed]

Bunk, O.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[Crossref]

Buzmakov, A. V.

Chatterjee, S.

S. Chatterjee, Y. P. Kumar, and B. Bhaduri, “Measurement of surface figure of plane optical surfaces with polarization phase-shifting Fizeau interferometer,” Opt. Laser Technol. 39(2), 268–274 (2007).
[Crossref]

Cheng, Z.

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Cheung, C. F.

C. F. Cheung and W. B. Lee, “Characterization of nanosurface generation in single-point diamond turning,” Int. J. Mach. Tools Manuf. 41(6), 851–875 (2001).
[Crossref]

C. F. Cheung and W. B. Lee, “A theoretical and experimental investigation of surface roughness formation in ultra-precision diamond turning,” Int. J. Mach. Tools Manuf. 40(7), 979–1002 (2000).
[Crossref]

Chu, Y.

Chvykov, V.

Collins, S. A.

L. Li, S. A. Collins, and A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” J. Manuf. Sci. Eng. 132(2), 021002 (2010).
[Crossref]

David, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[Crossref]

Demos, S. G.

Deutsch, I. H.

G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, “Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75(15), 2823–2826 (1995).
[Crossref] [PubMed]

Diaz, A.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[Crossref]

Fairman, P. S.

Fang, F.

Farrant, D. I.

Feit, M. D.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

Forbes, G.

Fukui, R.

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
[Crossref] [PubMed]

Gan, Z.

Gao, H.

Gatzke, M.

G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, “Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75(15), 2823–2826 (1995).
[Crossref] [PubMed]

Giltner, D. M.

D. M. Giltner, R. W. McGowan, and S. A. Lee, “Atom interferometer based on Bragg scattering from standing light waves,” Phys. Rev. Lett. 75(14), 2638–2641 (1995).
[Crossref] [PubMed]

Grünzweig, C.

C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
[Crossref]

Gwalt, G.

F. Siewert, J. Buchheim, G. Gwalt, R. Bean, and A. P. Mancuso, “On the characterization of a 1 m long, ultra-precise KB-focusing mirror pair for European XFEL by means of slope measuring deflectometry,” Rev. Sci. Instrum. 90(2), 021713 (2019).
[Crossref] [PubMed]

Hachisu, Y.

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

Handa, S.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

He, C. L.

Huang, Q.

Inagaki, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Inoue, I.

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

Inoue, N.

Inoue, T.

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

Inubushi, Y.

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B. G. Oldaker, A. H. Miklich, D. E. Pritchard, D. E. Pritchard, and Mar- PJ p tin, “Bragg scattering of atoms from a standing light wave,” Phys. Rev. Lett. 60(6), 515–518 (1988).
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J. Kim, H.-Y. Kim, J. Park, S. Kim, S. Kim, S. Rah, J. Lim, and K. H. Nam, “Focusing X-ray free-electron laser pulses using Kirkpatrick-Baez mirrors at the NCI hutch of the PAL-XFEL,” J. Synchrotron Radiat. 25(Pt 1), 289–292 (2018).
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Shore, B. W.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
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M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
[Crossref]

Staggs, M.

Stuart, B. C.

B. C. Stuart, M. D. Feit, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Laser-induced damage in dielectrics with nanosecond to subpicosecond pulses,” Phys. Rev. Lett. 74(12), 2248–2251 (1995).
[Crossref] [PubMed]

Sung, J. H.

Tamasaku, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Tanaka, T.

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

Teng, H.

Togashi, T.

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

Tono, K.

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

Ueda, H.

Walsh, C. J.

Wang, C.

Wang, X.

Wang, Z.

Wei, Z.

Wen, M.

Xie, C.

Xu, L.

Xu, Y.

Xu, Z.

Yabashi, M.

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Yamada, J.

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

Yamakawa, D.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Yamakawa, K.

Yamamura, K.

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Yamauchi, K.

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Yang, J. M.

Yanovsky, V.

Yi, A. Y.

L. Li, S. A. Collins, and A. Y. Yi, “Optical effects of surface finish by ultraprecision single point diamond machining,” J. Manuf. Sci. Eng. 132(2), 021002 (2010).
[Crossref]

Yin, D.

Yokoyama, H.

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Yoo, J. Y.

Yoon, J. W.

Yu, L.

Yu, T. J.

Yumoto, H.

S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
[Crossref] [PubMed]

H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
[Crossref]

Zhang, Q.

Zhang, X.

Zong, W. J.

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J. Kim, H.-Y. Kim, J. Park, S. Kim, S. Kim, S. Rah, J. Lim, and K. H. Nam, “Focusing X-ray free-electron laser pulses using Kirkpatrick-Baez mirrors at the NCI hutch of the PAL-XFEL,” J. Synchrotron Radiat. 25(Pt 1), 289–292 (2018).
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C. David, J. Bruder, T. Rohbeck, C. Grünzweig, C. Kottler, A. Diaz, O. Bunk, and F. Pfeiffer, “Fabrication of diffraction gratings for hard X-ray phase contrast imaging,” Microelectron. Eng. 84(5-8), 1172–1177 (2007).
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H. Mimura, H. Yumoto, S. Matsuyama, T. Koyama, K. Tono, Y. Inubushi, T. Togashi, T. Sato, J. Kim, R. Fukui, Y. Sano, M. Yabashi, H. Ohashi, T. Ishikawa, and K. Yamauchi, “Generation of 10(20) W cm(-2) hard X-ray laser pulses with two-stage reflective focusing system,” Nat. Commun. 5(1), 3539 (2014).
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H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7(1), 43–47 (2013).
[Crossref]

Nat. Phys. (1)

H. Mimura, S. Handa, T. Kimura, H. Yumoto, D. Yamakawa, H. Yokoyama, S. Matsuyama, K. Inagaki, K. Yamamura, Y. Sano, K. Tamasaku, Y. Nishino, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Breaking the 10 nm barrier in hard-X-ray focusing,” Nat. Phys. 6(2), 122–125 (2010).
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[Crossref] [PubMed]

M. Lenzner, J. Krüger, S. Sartania, Z. Cheng, Ch. Spielmann, G. Mourou, W. Kautek, and F. Krausz, “Femtosecond optical breakdown in dielectrics,” Phys. Rev. Lett. 80(18), 4076–4079 (1998).
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S. Matsuyama, T. Inoue, J. Yamada, J. Kim, H. Yumoto, Y. Inubushi, T. Osaka, I. Inoue, T. Koyama, K. Tono, H. Ohashi, M. Yabashi, T. Ishikawa, and K. Yamauchi, “Nanofocusing of X-ray free-electron laser using wavefront-corrected multilayer focusing mirrors,” Sci. Rep. 8(1), 17440 (2018).
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Figures (7)

Fig. 1
Fig. 1 (a) Two-dimensional (2D) surface image with circular waviness composed of 25 periodic structures (waviness 2 mm, modulation depth ± 30 nm). (b) Line profiles for the black dotted line on the 2D surface image. Three of the tested samples exhibit a sinusoidal waviness equal to 2 mm and modulation depths of ± 50 nm (black), ± 30 nm (red), and ± 15 nm (blue). One of the tested samples has a flat surface (cyan).
Fig. 2
Fig. 2 Experimental configuration for the observation of the laser beam profile at increasing propagating distances after the reflection on the surface of the sample. The interference formed from the beam propagation of the 0th, 1st, and −1st beam modes caused by Bragg scattering is observed in the beam profile. The beam profiler is placed at many positions along the beam’s propagation path to observe the variation of the interference patterns within the beam profile for propagations at large distances.
Fig. 3
Fig. 3 Center intensity in the beam profile observed as a function of the variation of the propagation distance in the range of 10 to 250 cm after reduced collimation. Three of the tested samples have a waviness equal to 2 mm and modulation depths equal to ± 50 nm (black), ± 30 nm (red), and ± 15 nm (blue). One of the tested samples has a flat surface (cyan).
Fig. 4
Fig. 4 (a) Center intensity in the beam profile calculated by variation of the propagating distance from 10 to 250 cm after reduced collimation. All the values are normalized to the maximum value corresponding to the modulation depth of ± 50 nm. (b) Comparison between the experimental and simulation results for waviness of 2 mm and modulation depth of ± 30 nm. All the values are normalized to the maximum value corresponding to the modulation depth of ± 30 nm.
Fig. 5
Fig. 5 (a) 2D images of beam profiles measured at the propagating distances of 35 cm and 50 cm after collimation reduction for the sample with a waviness of 2 mm and height of ± 15 nm. (b) Intensity distributions of the two line profiles obtained along the horizontal and radial directions in the images of (a). (c) 2D images of beam profiles calculated at the propagating distances of 27.5 cm and 42.5 cm after collimation reduction for the sample with a waviness of 2 mm and height of ± 15 nm. (d) Intensity distributions of the two line profiles obtained along the horizontal and radial directions in the images of (c).
Fig. 6
Fig. 6 (a) Schematic of three wavefronts for each of the 0th, 1st, and −1st beam modes after the reflection on the surface of the sample. (b) Three propagation lines which exhibit periodic constructive interference are formed. The propagation line in black color (α(1, −1)) is formed by the 1st and −1st modes, the propagation line in red color (β(0, 1)) is formed by the 0th and the 1st modes, while the line in blue color (γ(0, −1)) is formed by the 0th and −1st modes during the beam propagation. (c) The peaks of line profiles (black and red colors) correspond to the positions of the constructive interference formed by the overlap of the three propagation lines.
Fig. 7
Fig. 7 Configurations of geometric rhombi formed by the overlaps of three propagation lines, such as α(1, −1), β(0, 1), and γ(0, −1), (a) before and (b) after the reduced collimation.

Equations (2)

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E out (x,y,z)= F 1 [H( ν x , ν y )F[ E in (x,y,z)]].
( x Δ θ )=( 1 0 1 f 2 1 )( 1 d 0 1 )( 1 0 1 f 1 1 )( x Δθ )=( x d f x+dΔθ x 1 f 2 d f 1 f 2 x+ d f 2 Δθ 1 f 1 x+Δθ ).

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